Noether's theorem for fractional variational problems of variable order

被引：60

作者：

Odzijewicz, Tatiana ^{[1
]}

Malinowska, Agnieszka B. ^{[2
]}

Torres, Delfim F. M. ^{[1
]}

机构：

[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat, P-3810193 Aveiro, Portugal

[2] Bialystok Tech Univ, Fac Comp Sci, PL-15351 Bialystok, Poland

来源：

CENTRAL EUROPEAN JOURNAL OF PHYSICS | 2013年 / 11卷 / 06期

关键词：

variable order fractional integrals; variable order fractional derivatives; fractional variational analysis; Euler-Lagrange equations; Noether's theorem; FORMULATION; MECHANICS; CALCULUS; DYNAMICS; ENERGY;

D O I：

10.2478/s11534-013-0208-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether's theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

引用

页码：691 / 701

页数：11

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